Question

Let $X \sim N(\mu X, \sigma _X ^2)$ and $Y \sim N(\mu _y, \sigma _y ^2)$ Which of the following is/are NOT correct?

• A. The area F(X)= \frac1{\sigma _x \sqrt{2\pi}}$$\int_{-\infty}^{\mu_x} e^{-\frac1{2}(\frac{X-\mu_x}{\sigma_x})^2} dx is 1.
• B. The areas under the normal probability curve between the ordinates at $\mu_x ± 3\sigma_x$ , and $\mu_y ± 3\sigma_y$ are 0.9544 and 0.9973, respectively.
• C. For variable X,
  Quartile Deviation: Mean Absolute Deviation: Standard Deviation ≅ $\frac2{3} \sigma_x : \frac4{5}\sigma_x : \sigma_x$
• D. If X and Y are independent, then $(X-Y) \sim N(\mu_x - \mu_y, σ^2_x +σ^2_y)$.

Answer 1

Answer: (A), (B)

The area F(X)= \frac1{\sigma _x \sqrt{2\pi}}$$\int_{-\infty}^{\mu_x} e^{-\frac1{2}(\frac{X-\mu_x}{\sigma_x})^2} dx is 1.

Answer 2

The correct option is (A): The area F(X)= \frac1{\sigma _x \sqrt{2\pi}}$$\int_{-\infty}^{\mu_x} e^{-\frac1{2}(\frac{X-\mu_x}{\sigma_x})^2} dx is 1. and (B): The areas under the normal probability curve between the ordinates at $\mu_x ± 3\sigma_x$ , and $\mu_y ± 3\sigma_y$ are 0.9544 and 0.9973, respectively.